实战项目 2:突破策略

Methods and ideas to be covered in this notebook:

  1. Compute the highs and lows in a window
  2. Compute long and short signal
    • Filter out repeated long or short signals within the lookahead_days
  3. Evaluate how many days to short or long the stocks
    • get the close price days ahead in time
    • calculate future log returns between the closing price and the lookahead price
    • generate the signal returns
  4. Test for significance
    • to deal with outliers: compare returns to normal distributions with the same means and deviations for each signal return distribution using KolMogorov-Smirnov Test
    • find outliers based on the result from K-S test and compare different day signals returns without outliers to normal distribution

加载软件包

In [1]:
import pandas as pd
import numpy as np
import helper
import project_helper_zh
import project_tests
%matplotlib inline

市场数据

加载数据

虽然使用真实数据能够带来实践经验,但是并不能在一个实战项目中涵盖所有概念。为了解决这个问题,我们将创建几个虚拟股票。我们假设开采的公司利润丰厚。这个行业的所有公司都是虚构的。它们代表了一个增长迅速的行业,之后演示时会用到这个行业。

In [2]:
df_original = pd.read_csv('eod-quotemedia.csv', parse_dates=['date'], index_col=False)

# Add TB sector to the market
df = df_original
df = pd.concat([df] + project_helper_zh.generate_tb_sector(df[df['ticker'] == 'AAPL']['date']), ignore_index=True)

close = df.reset_index().pivot(index='date', columns='ticker', values='adj_close')
high = df.reset_index().pivot(index='date', columns='ticker', values='adj_high')
low = df.reset_index().pivot(index='date', columns='ticker', values='adj_low')

print('Loaded Data')
Loaded Data

查看数据

为了查看这些二维矩阵是什么样的,我们看看收盘价矩阵。

In [3]:
close
Out[3]:
ticker A AAL AAP AAPL ABBV ABC ABT ACN ADBE ADI ... XL XLNX XOM XRAY XRX XYL YUM ZBH ZION ZTS
date
2013-07-01 29.99418563 16.17609308 81.13821681 53.10917319 34.92447839 50.86319750 31.42538772 64.69409505 46.23500000 39.91336014 ... 27.66879066 35.28892781 76.32080247 40.02387348 22.10666494 25.75338607 45.48038323 71.89882693 27.85858718 29.44789315
2013-07-02 29.65013670 15.81983388 80.72207258 54.31224742 35.42807578 50.69676639 31.27288084 64.71204071 46.03000000 39.86057632 ... 27.54228410 35.05903252 76.60816761 39.96552964 22.08273998 25.61367511 45.40266113 72.93417195 28.03893238 28.57244125
2013-07-03 29.70518453 16.12794994 81.23729877 54.61204262 35.44486235 50.93716689 30.72565028 65.21451912 46.42000000 40.18607651 ... 27.33445191 35.28008569 76.65042719 40.00442554 22.20236479 25.73475794 46.06329899 72.30145844 28.18131017 28.16838652
2013-07-05 30.43456826 16.21460758 81.82188233 54.17338125 35.85613355 51.37173702 31.32670680 66.07591068 47.00000000 40.65233352 ... 27.69589920 35.80177117 77.39419581 40.67537968 22.58516418 26.06075017 46.41304845 73.16424628 29.39626730 29.02459772
2013-07-08 30.52402098 16.31089385 82.95141667 53.86579916 36.66188936 52.03746147 31.76628544 66.82065546 46.62500000 40.25645492 ... 27.98505704 35.20050655 77.96892611 40.64620776 22.48946433 26.22840332 46.95062632 73.89282298 29.57661249 29.76536472
2013-07-09 30.68916447 16.71529618 82.43619048 54.81320389 36.35973093 51.69535307 31.16522893 66.48866080 47.26000000 40.69632003 ... 28.31939579 35.50113886 78.89018496 40.80179133 22.48946433 26.58233774 47.28094525 73.70108798 28.91218282 29.80384612
2013-07-10 31.17771395 16.53235227 81.99032166 54.60295791 36.85493502 52.28710814 31.16522893 66.71298151 47.25000000 41.10979324 ... 27.95794850 36.39419366 78.45068533 40.71427558 22.96796358 26.98284247 47.08340158 74.00785631 28.32368796 29.86156823
2013-07-11 31.45983407 16.72492481 82.00022986 55.45406479 37.08155384 53.72026495 31.85599537 67.47567196 47.99000000 42.22705062 ... 28.50011944 37.00430040 78.83102155 41.01571874 23.23113816 27.03872686 46.54333492 74.93774876 27.84909533 29.74612402
2013-07-12 31.48047700 16.90786872 81.91105609 55.35309481 38.15724076 53.98840397 31.81096287 67.76280247 48.39000000 42.53495620 ... 28.92482002 38.00346072 78.94089646 40.83096325 23.49431274 27.08529718 45.96422730 75.68549560 28.44708204 30.15979909
2013-07-15 31.72819223 17.10044125 82.61453801 55.47379158 37.79303181 53.84971137 31.95506689 68.41781897 48.12000000 42.57894271 ... 29.27723113 38.17146113 78.81411772 40.84068723 23.54216266 27.06666905 46.69299195 76.27027369 28.77929688 30.38106716
2013-07-16 31.59057266 17.28338516 81.62371841 55.83133953 37.10696377 53.88669607 32.15320992 67.55642741 47.48500000 42.68451033 ... 29.04229039 38.27314559 78.85637730 40.86013517 23.27898808 26.61959399 46.56936223 76.81670381 28.06740794 29.97701243
2013-07-17 31.38414330 17.76481650 80.74188897 55.84626440 37.23401341 54.06237335 32.26128793 67.43978064 48.04000000 42.80767257 ... 29.18686931 38.48977769 78.99160796 40.93792696 23.18328823 26.66616431 46.45874617 78.30261578 28.06740794 29.81346647
2013-07-18 31.58369168 17.73593062 81.74261676 56.03418797 37.53893253 53.91443458 32.15320992 67.69101984 48.19000000 42.52615889 ... 29.55735279 40.52346684 79.76918424 41.22964615 23.49431274 26.94558622 46.97929234 78.81069986 28.77929688 29.64992051
2013-07-19 31.79012104 17.55298671 81.45527908 55.15063572 37.70833205 54.37674323 32.30632044 67.49361761 48.07000000 42.20945601 ... 29.71096789 40.54999322 80.43688561 41.24909410 23.20721320 26.81518933 46.90121042 81.16898043 28.99760949 29.09194018
2013-07-22 32.20297975 17.47595770 81.99032166 55.32713852 38.08948096 54.54317435 32.24327493 67.29621538 48.28000000 42.17426681 ... 29.84651063 40.59420386 80.14952046 41.49219343 23.47038778 26.88970184 46.50429396 81.02518181 29.27287321 29.12080123
2013-07-23 31.97590746 17.37967143 81.94078068 54.37713815 37.53046256 53.28569482 33.03584705 66.62325323 48.07000000 42.56134810 ... 29.13265221 40.52346684 80.46224136 41.32688588 23.42253785 26.74067682 45.82758393 81.00601167 28.38063907 28.91877387
2013-07-24 32.17545584 17.81295964 80.78152175 57.17003539 36.96297418 52.49052395 32.82869752 66.14769330 47.80000000 42.42938857 ... 28.73506019 40.24051879 80.28475112 41.15185437 23.51823770 26.62890805 46.49128030 80.56503316 28.53250871 28.76484826
2013-07-25 32.10664605 18.13070432 81.46518728 56.90917464 37.47117273 53.26720248 32.94578204 65.62726924 47.79000000 42.88684829 ... 29.02421802 41.05399445 80.26784729 40.91847901 23.44646282 26.85244558 46.91422407 79.47217195 28.19080202 29.36130999
2013-07-26 31.37726233 18.38104862 81.88133151 57.23233050 37.93702140 54.06237335 33.12591207 65.60932358 47.64000000 42.71969954 ... 29.11457985 40.83294128 80.11571280 40.98654682 23.18328823 26.70342056 48.15052124 80.98684153 28.04842424 29.27472684
2013-07-29 31.19835688 18.51584940 81.57417743 58.11484449 38.16571074 53.98840397 33.08988606 64.93636143 47.17000000 42.66691573 ... 28.92482002 40.38199282 79.47336717 40.93792696 23.08758839 26.50782523 47.83819353 80.16240164 27.71620940 28.94763492
2013-07-30 30.86118893 18.48696352 81.43546269 58.83253602 37.86079161 53.84046520 33.21597708 66.16563896 47.36000000 43.04519972 ... 28.38264907 40.88599404 79.28742502 41.08378656 23.06366342 23.78811863 47.53237266 79.55844670 27.77316051 28.96206545
2013-07-31 30.77861719 18.63139292 81.73270857 58.73000866 38.52144972 53.87744989 32.99081455 66.22844876 47.28000000 43.44107832 ... 28.32843198 41.28388974 79.23671352 41.69639686 23.20721320 23.21996075 47.44778390 80.02819050 28.13385091 28.74031861
2013-08-01 31.68002538 18.66027880 82.66407899 59.26808264 38.32664028 54.36749706 33.17995107 67.16162295 47.70000000 43.93372725 ... 28.97000093 41.69062757 78.37461808 41.71584481 23.70963740 23.46212640 48.08545297 80.97725310 28.61793539 29.07775945
2013-08-02 31.91397865 18.21736196 82.70371177 60.02912118 38.38593011 54.07161953 33.09889256 66.92832940 47.45000000 43.87214613 ... 28.87060292 41.12473146 77.71536862 41.78391262 23.92496206 23.53663891 48.40428750 80.52668616 28.61793539 29.82977047
2013-08-05 31.61121560 18.45807764 82.64426260 60.92591114 37.86926159 54.58015904 32.82869752 66.60530757 47.63000000 43.61702437 ... 28.60855363 41.00978381 77.41109964 41.52136535 24.09243679 23.54595298 48.68408107 80.46916901 28.39962278 30.12864664
2013-08-06 31.70754930 18.21736196 82.41637409 60.38082896 38.01325118 54.23805064 32.51346997 65.72597036 47.39000000 43.47626753 ... 28.34650434 40.50305117 77.30967665 41.40467767 23.85318717 23.68566393 48.15052124 79.56803513 27.88706274 30.01295264
2013-08-07 31.84516887 18.16921883 81.53454465 60.34578796 37.75068193 54.31202002 32.36035945 65.50164964 47.10000000 43.23874037 ... 28.19288924 40.52972131 77.19980174 41.22964615 23.61393755 23.19201856 48.07243931 79.17498438 27.57383161 30.11900548
2013-08-08 31.54928679 18.27513373 80.90042011 60.22638901 38.16571074 55.11643707 32.35135295 65.48370398 47.51000000 43.19475386 ... 28.02120177 40.52083127 77.57168605 41.57970919 23.87711213 23.26653107 48.21558951 79.84604489 28.01994868 30.11900548
2013-08-09 31.80388300 17.90924591 82.40646589 59.36939001 37.86926159 55.00548300 32.32433344 65.97720956 47.18000000 43.10678084 ... 27.86758667 40.27190997 77.20825366 41.39495370 23.99673694 23.26653107 48.41079433 79.15581519 27.99147312 29.80084697
2013-08-12 31.96214550 18.12107570 81.69307578 61.05595360 38.14877079 54.24729681 32.33333995 65.31322023 47.20000000 43.46747023 ... 27.76818866 40.35192038 76.50187303 41.53108932 24.28383649 23.12682011 48.45634212 78.90656401 28.10537535 29.24165929
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2017-05-19 55.50327007 44.83282860 151.06072036 150.70113045 63.42995100 87.59994036 42.31486674 118.75601310 136.43000000 79.14250576 ... 40.43133035 65.31985198 78.78898294 61.13598414 26.81497802 51.24320268 68.90686651 116.46112494 39.54646594 59.92967369
2017-05-22 55.45382835 45.81435227 146.97179877 151.61679784 63.29454092 87.91434122 42.87370534 120.45421034 138.86000000 79.97056004 ... 40.86051697 66.15263846 79.13518133 62.09836493 26.73836380 51.49936943 69.83126290 116.57989212 39.65494752 59.92967369
2017-05-23 58.00502088 46.26049939 140.27992953 151.42972601 63.68142686 87.62941544 42.82468441 119.90450488 139.52000000 79.84391644 ... 41.31896631 62.67453024 79.41406336 62.65396622 26.62344247 52.19890171 69.74275686 116.59968666 40.76934918 61.04261076
2017-05-24 58.56865644 46.36955757 132.66057320 150.97681525 63.76847620 88.39576754 42.67762162 119.70818149 141.12000000 79.99978549 ... 41.61159355 63.13501218 79.13518133 62.23726525 26.89159225 52.01106475 70.75565928 117.87643393 40.13818363 61.90712437
2017-05-25 58.63787484 47.60885514 131.61341035 151.49864721 64.14569000 89.51582062 43.08939743 120.83704093 142.85000000 80.21410542 ... 42.29439045 64.10496348 78.61588375 62.57459460 26.77667091 51.53652928 70.93267135 118.07437924 40.31569894 62.18535864
2017-05-26 58.84553005 48.32269053 133.79749286 151.24265417 63.89421413 89.40774532 43.83451556 120.63090138 141.89000000 80.67197073 ... 42.23586500 64.51645797 78.42355131 62.22734380 26.81497802 50.82472608 70.89333534 118.00509838 39.89163460 62.21516946
2017-05-30 59.69592756 47.54936885 132.63065426 151.30172949 63.85552554 89.43722040 44.11883696 121.49472426 142.41000000 82.61059193 ... 42.33340741 64.38909063 77.99080333 62.12812929 27.12143491 51.20039999 71.20802347 117.21331713 39.31964082 61.86737662
2017-05-31 59.66626253 47.99551598 133.26892494 150.40575387 63.85552554 90.16427240 44.76591323 122.18185609 141.86000000 83.54580618 ... 42.61628041 65.35904193 77.41380602 63.02105992 27.08312780 51.54641544 71.43420556 117.98530385 39.51688006 61.88725050
2017-06-01 60.05190791 48.63003633 136.72954883 150.81928108 64.52290380 91.51030109 45.19729742 122.98678196 141.38000000 80.08746182 ... 42.54800072 65.30025701 77.60613845 63.55681830 27.19804914 51.84300011 72.60445204 121.40975776 39.99025421 62.24498027
2017-06-02 60.13101466 49.09601221 137.42765739 153.05429719 65.04519983 91.94260228 45.58946486 123.42850956 143.48000000 78.82102586 ... 42.21635651 65.52559923 76.45214383 63.94375491 27.12143491 52.39662482 72.76179611 122.66671050 39.54646594 62.10586314
2017-06-05 59.72559259 49.31412858 135.20368297 151.55772252 65.29667569 91.68715157 45.70711509 124.25306776 143.59000000 76.71679380 ... 41.72864445 65.79013140 77.04837438 63.39807508 26.73836380 52.59434793 72.96831019 122.65681324 39.90149656 62.27479108
2017-06-06 59.42894229 49.31412858 130.94522072 152.06970859 65.64487304 90.08567218 45.45220625 124.00766354 143.03000000 78.03193884 ... 41.48478841 66.24081585 78.09658617 63.05082428 26.81497802 52.09015400 73.08631824 122.89434761 39.70425733 62.58283617
2017-06-07 59.95302448 50.42453920 130.26705812 152.97553010 66.49602213 90.32147283 45.64828997 124.22361925 143.62000000 79.18147302 ... 41.45552569 66.49555053 77.80808751 63.10043153 26.96820647 52.85138798 73.02731422 123.07249839 39.90149656 62.86107043
2017-06-08 59.47838401 50.98965889 125.57975776 152.60138644 66.50569428 89.96777186 45.80515695 123.85060483 142.63000000 80.75863709 ... 41.18240693 66.69150029 77.52920548 62.95160976 26.81497802 52.97002185 72.74212810 123.88407418 40.81865898 62.18535864
2017-06-09 58.54887976 49.83959075 128.01316475 146.68400898 67.38585980 90.48849829 46.36399555 123.50703891 138.05000000 76.99695384 ... 41.52380538 64.07557102 78.98131538 62.84247379 26.58513535 53.35558192 71.88656975 123.72571793 41.75554533 62.19529558
2017-06-12 58.33133621 49.05635469 130.59616644 143.17887358 67.25044972 90.74394899 46.24634532 123.97821503 137.25000000 78.11370356 ... 41.13363573 62.92926493 79.75064513 62.25710816 27.04482069 53.40501269 70.71632326 123.71582066 42.33740107 61.45996216
2017-06-13 58.61809816 49.02661155 131.27432905 144.33084223 67.38585980 91.37275071 46.53066671 124.73406004 139.09000000 79.57331502 ... 41.54331386 63.46812677 79.77949499 62.78294509 26.85328513 53.17763111 71.46370757 124.18099215 42.53464030 61.67360633
2017-06-14 58.71698159 48.96712526 130.23713918 142.92288054 68.20799244 92.25700314 46.70714206 124.91075109 138.25000000 79.28922957 ... 41.97472897 63.56610164 78.92361565 63.22941040 26.54682824 53.04911109 71.82756572 124.30965660 42.63325991 61.94235833
2017-06-15 58.54887976 48.68952261 130.79562603 142.06628846 68.28536963 92.77772957 47.17774299 124.69479537 137.52000000 78.12349961 ... 42.63165652 63.54650667 79.10633146 62.81270944 26.61386569 53.34569576 71.40470355 124.54719098 42.27822930 62.10161877
2017-06-16 58.84553005 48.37226243 129.80830106 140.07741950 68.72061632 90.91097444 47.26598066 125.21505233 137.84000000 78.40758506 ... 43.18073029 63.42893681 80.28917595 63.19964605 27.29381692 53.43467116 71.57188162 124.62636910 42.49519245 62.26087921
2017-06-19 59.87391774 49.23481354 129.24981421 144.08469508 69.00110863 92.10962773 47.93266531 125.42119188 140.35000000 78.73085471 ... 43.23955963 64.56544541 79.58716256 63.47744669 27.57154347 53.55330503 72.70279208 125.78434918 42.76146542 62.73866054
2017-06-20 59.65637419 47.61876952 123.24608056 142.77519225 68.88504285 91.61837639 47.81501508 124.20398692 140.91000000 77.58471685 ... 43.33760851 63.93840619 79.15441457 62.85239525 27.13101169 53.26660652 72.68312408 125.91301364 42.36698695 62.70879921
2017-06-21 59.12240366 48.01534474 119.84529455 143.62193844 69.00110863 93.94690777 47.61893136 124.77332472 144.24000000 78.34880876 ... 43.15131563 64.78099015 78.31776847 63.26909621 26.70005669 52.93047722 73.16499028 127.43719255 41.74568337 62.70879921
2017-06-22 59.93324780 48.55072128 120.43399427 143.38563718 70.78078399 94.68378480 48.30522438 119.83579169 143.69000000 79.66147947 ... 42.42575385 65.23167459 77.97157008 63.32862492 26.78624769 53.23694805 73.30266633 128.29986262 41.71609749 63.21644187
2017-06-23 59.10262697 48.21363235 119.47610998 144.02561977 70.25848796 94.14340831 48.11894484 120.48365885 145.41000000 79.88678863 ... 42.56302230 66.16243594 78.48125104 63.33854637 27.23635625 53.71148352 73.57801845 128.00239018 41.35120491 62.48981610
2017-06-26 58.57854478 48.36234805 121.52159207 143.57270901 70.35520945 94.31043377 47.95227368 120.09101209 144.96000000 78.92677572 ... 42.76892496 65.99587865 78.12543603 63.56673975 27.95461459 54.05749897 73.49934641 127.97264293 41.75554533 62.43009343
2017-06-27 58.22256443 48.08474540 121.69121741 141.51491885 70.01668424 93.85848253 47.71697322 119.94376955 142.54000000 76.54633554 ... 43.14151074 63.78164638 78.00041995 63.92391201 27.75350225 53.87954816 72.74212810 127.16946735 41.95278457 62.46990854
2017-06-28 58.73675827 48.82832394 116.45278767 143.58255490 70.52930812 94.69360982 47.53069368 121.46527575 143.81000000 77.58471685 ... 43.30819385 64.67321778 78.40431807 64.82428373 28.28980181 54.34419748 72.91914017 127.42727680 42.37684891 62.65903032
2017-06-29 58.27398382 49.19515602 115.79424221 141.46568942 70.10373358 94.08445815 47.77579833 120.72906307 141.24000000 76.15449354 ... 43.27877918 62.88027749 77.60613845 64.10898129 28.12560699 54.27499439 72.23075989 126.81250043 43.38276899 62.21111032
2017-06-30 58.77942143 49.88916265 116.33305213 141.80044954 70.13275003 92.87597984 47.65814810 121.40637874 141.44000000 76.21326984 ... 42.94541296 63.01744232 77.63498832 64.41695873 27.74892476 54.79896064 72.53561401 127.31820357 43.30387330 62.09166499

1009 rows × 519 columns

股票示例

我们通过收盘价矩阵看看单个股票是什么样的。对于此示例以及此项目中的后续其他示例,我们将使用 Apple 的股票 (AAPL)。如果要绘制所有股票的图形,那么信息太多了。

In [4]:
apple_ticker = 'AAPL'
project_helper_zh.plot_stock(close[apple_ticker], '{} Stock'.format(apple_ticker))

Alpha 研究流程

在此项目中,你需要编写并评估“突破”信号。务必要了解这些步骤在 alpha 研究工作流程中所处的阶段。交易信号中的信噪比很低,很容易过拟合噪点。所以不建议立即开始信号编程。为了避免过拟合,建议先提出一般的假设,即在处理任何数据之前,你应该能够回答以下问题:

什么样的市场或投资者行为特征会导致一直出现的异常,并且我的信号可以使用这种异常?

理想情况下,在开始编程和评估信号本身之前,应该能够测试假设条件。工作流程如下所示:

image

在此项目中,我们假定前三个步骤(观察和研究、提出假设、验证假设)已经完成。对于此项目,你将用到以下假设:

  • 在没有重大新闻或出现明显的投资者交易兴趣时,股票会在一定范围内波动。
  • 为了根据这种遵守一定范围规律的行为获利,交易者会定期卖出/做空范围顶部的股票并买入/做多范围底部的股票。这种行为进一步加强了这个范围的存在。
  • 当股票因为重大新闻或大型投资者带来的市场压力而突破这个范围时:
    • 流动性交易者在范围界限处提供流动性,他们希望平仓来减少损失,因此会加大超出范围的影响,并且
    • 超出范围会吸引其他投资者;由于羊群效应 (例如从众行为),这些投资者建立的头寸会倾向于延续这种趋势。

我们利用这种假设开始编程吧。

计算窗口中的高低价格

我们将根据高低价格创建突破策略。在此部分,请实现 get_high_lows_lookback 以获得窗口期内的最高价格和最低价格。变量 lookback_days 包含要查看的过去日期,请勿包含当前日期。

In [5]:
def get_high_lows_lookback(high, low, lookback_days):
    """
    Get the highs and lows in a lookback window.
    
    Parameters
    ----------
    high : DataFrame
        High price for each ticker and date
    low : DataFrame
        Low price for each ticker and date
    lookback_days : int
        The number of days to look back
    
    Returns
    -------
    lookback_high : DataFrame
        Lookback high price for each ticker and date
    lookback_low : DataFrame
        Lookback low price for each ticker and date
    """
    # .shift(1) makes sure it does not include the current day
    return high.shift(1).rolling(lookback_days).max(), low.shift(1).rolling(lookback_days).min()

project_tests.test_get_high_lows_lookback(get_high_lows_lookback)
Tests Passed

查看数据

我们使用 get_high_lows_lookback 获取过去 50 天的高低价格,并与相应的股票进行比较。与之前一样,我们将以 Apple 股票为例。

In [6]:
lookback_days = 50
lookback_high, lookback_low = get_high_lows_lookback(high, low, lookback_days)
project_helper_zh.plot_high_low(
    close[apple_ticker],
    lookback_high[apple_ticker],
    lookback_low[apple_ticker],
    'High and Low of {} Stock'.format(apple_ticker))

计算做多和做空信号

根据生成的最高和最低价格信号,利用突破策略创建做多和做空信号。实现 get_long_short 以生成以下信号:

信号 条件
-1 最低价 > 收盘价
1 最高价 < 收盘价
0 其他

在此图表中,收盘价close 参数。最低价最高价get_high_lows_lookback 生成的 lookback_highlookback_low 参数。

In [7]:
def get_long_short(close, lookback_high, lookback_low):
    """
    Generate the signals long, short, and do nothing.
    
    Parameters
    ----------
    close : DataFrame
        Close price for each ticker and date
    lookback_high : DataFrame
        Lookback high price for each ticker and date
    lookback_low : DataFrame
        Lookback low price for each ticker and date
    
    Returns
    -------
    long_short : DataFrame
        The long, short, and do nothing signals for each ticker and date
    """
    long = (close > lookback_high).astype('int')
    short = (close < lookback_low).astype('int')*-1
    
    return long + short

project_tests.test_get_long_short(get_long_short)
Tests Passed

查看数据

我们将你创建的信号与收盘价进行比较。此图表将显示很多信号。实际上太多了。我们将在下个问题中讨论如何滤除多余的信号。

In [8]:
signal = get_long_short(close, lookback_high, lookback_low)
project_helper_zh.plot_signal(
    close[apple_ticker],
    signal[apple_ticker],
    'Long and Short of {} Stock'.format(apple_ticker))

滤除信号

重复信号太多了!如果我们已经做空股票,再有一个做空信号并没有多大作用。如果上一个信号是做多信号,那么再有其他做多信号也一样多余。

实现 filter_signals 以滤除 lookahead_days 中重复出现的做多或做空信号。如果上个信号一样,将信号变成 0 (什么也不做信号)。例如,假设有一个如下所示的股票时序:

[1, 0, 1, 0, 1, 0, -1, -1]

运行 filter_signals 并向前看 3 天会将信号变成:

[1, 0, 0, 0, 1, 0, -1, 0]

为了帮助你实现该函数,我们提供了 clear_signals 函数。它会删除窗口中上个信号之后的所有信号。例如,假设将 clear_signals 的窗口大小设为 3,它会将以下做多信号序列:

[0, 1, 0, 0, 1, 1, 0, 1, 0]

变成

[0, 1, 0, 0, 0, 1, 0, 0, 0]

clear_signals 仅接受信号类型一样的序列,其中 1 表示信号,0 表示没有信号。不能将做多和做空信号混合到一起。请使用此函数实现 filter_signals

在实现 filter_signals 时,不建议寻找向量化解。应该针对每列使用 iterrows

In [9]:
def clear_signals(signals, window_size):
    """
    Clear out signals in a Series of just long or short signals.
    
    Remove the number of signals down to 1 within the window size time period.
    
    Parameters
    ----------
    signals : Pandas Series
        The long, short, or do nothing signals
    window_size : int
        The number of days to have a single signal       
    
    Returns
    -------
    signals : Pandas Series
        Signals with the signals removed from the window size
    """
    # Start with buffer of window size
    # This handles the edge case of calculating past_signal in the beginning
    clean_signals = [0]*window_size
    
    for signal_i, current_signal in enumerate(signals):
        # Check if there was a signal in the past window_size of days
        has_past_signal = bool(sum(clean_signals[signal_i:signal_i+window_size]))
        # Use the current signal if there's no past signal, else 0/False
        clean_signals.append(not has_past_signal and current_signal)
        
    # Remove buffer
    clean_signals = clean_signals[window_size:]

    # Return the signals as a Series of Ints
    return pd.Series(np.array(clean_signals).astype(np.int), signals.index)


def filter_signals(signal, lookahead_days):
    """
    Filter out signals in a DataFrame.
    
    Parameters
    ----------
    signal : DataFrame
        The long, short, and do nothing signals for each ticker and date
    lookahead_days : int
        The number of days to look ahead
    
    Returns
    -------
    filtered_signal : DataFrame
        The filtered long, short, and do nothing signals for each ticker and date
    """
    f_signal = signal.copy()
    for sector, row in (signal.iteritems()):
        long = row.copy()
        short = row.copy()
        long[long<0] = 0
        short[short>0] = 0
        f_signal[sector] = clear_signals(long, lookahead_days) + clear_signals(short, lookahead_days)
    
    return f_signal

project_tests.test_filter_signals(filter_signals)
Tests Passed

查看数据

下面看看之前的同一图表,但是删除了多余的信号。

In [10]:
signal_5 = filter_signals(signal, 5)
signal_10 = filter_signals(signal, 10)
signal_20 = filter_signals(signal, 20)
for signal_data, signal_days in [(signal_5, 5), (signal_10, 10), (signal_20, 20)]:
    project_helper_zh.plot_signal(
        close[apple_ticker],
        signal_data[apple_ticker],
        'Long and Short of {} Stock with {} day signal window'.format(apple_ticker, signal_days))

前瞻收盘价

创建了交易信号后,我们将判断应该做多或做空多少天的股票。在此问题中,请实现 get_lookahead_prices 以获取提前几天的收盘价。你可以从变量 lookahead_days 中获取天数。我们将在另一个问题中使用前瞻价格计算未来收益率。

In [11]:
def get_lookahead_prices(close, lookahead_days):
    """
    Get the lookahead prices for `lookahead_days` number of days.
    
    Parameters
    ----------
    close : DataFrame
        Close price for each ticker and date
    lookahead_days : int
        The number of days to look ahead
    
    Returns
    -------
    lookahead_prices : DataFrame
        The lookahead prices for each ticker and date
    """
    return close.shift(-lookahead_days)

project_tests.test_get_lookahead_prices(get_lookahead_prices)
Tests Passed

查看数据

我们使用 get_lookahead_prices 函数生成 5 天、10 天和 20 天的前瞻收盘价。

我们绘制几个月(而不是几年)的 Apple 股票图表,以便查看 5 天、10 天和 20 天前瞻期的区别。否则,在查看缩小的图表时,数据将挤在一起。

In [12]:
lookahead_5 = get_lookahead_prices(close, 5)
lookahead_10 = get_lookahead_prices(close, 10)
lookahead_20 = get_lookahead_prices(close, 20)
project_helper_zh.plot_lookahead_prices(
    close[apple_ticker].iloc[150:250],
    [
        (lookahead_5[apple_ticker].iloc[150:250], 5),
        (lookahead_10[apple_ticker].iloc[150:250], 10),
        (lookahead_20[apple_ticker].iloc[150:250], 20)],
    '5, 10, and 20 day Lookahead Prices for Slice of {} Stock'.format(apple_ticker))

前瞻价格收益率

实现 get_return_lookahead 以生成收盘价和前瞻价格间的对数收益率 。

In [13]:
def get_return_lookahead(close, lookahead_prices):
    """
    Calculate the log returns from the lookahead days to the signal day.
    
    Parameters
    ----------
    close : DataFrame
        Close price for each ticker and date
    lookahead_prices : DataFrame
        The lookahead prices for each ticker and date
    
    Returns
    -------
    lookahead_returns : DataFrame
        The lookahead log returns for each ticker and date
    """
    
    return np.log(lookahead_prices) - np.log(close)

project_tests.test_get_return_lookahead(get_return_lookahead)
Tests Passed

查看数据

我们将通过与上个问题相同的前瞻价格和部分 Apple 股票数据,查看前瞻收益率。

为了在股票图表上查看价格收益率,我们将添加第二个 y 轴。在查看此图表时,股价坐标轴将位于左侧,与之前的图表一样。价格收益率的坐标轴将位于右侧。

In [14]:
price_return_5 = get_return_lookahead(close, lookahead_5)
price_return_10 = get_return_lookahead(close, lookahead_10)
price_return_20 = get_return_lookahead(close, lookahead_20)
project_helper_zh.plot_price_returns(
    close[apple_ticker].iloc[150:250],
    [
        (price_return_5[apple_ticker].iloc[150:250], 5),
        (price_return_10[apple_ticker].iloc[150:250], 10),
        (price_return_20[apple_ticker].iloc[150:250], 20)],
    '5, 10, and 20 day Lookahead Returns for Slice {} Stock'.format(apple_ticker))

计算信号收益率

根据价格收益率生成信号收益率。

In [15]:
def get_signal_return(signal, lookahead_returns):
    """
    Compute the signal returns.
    
    Parameters
    ----------
    signal : DataFrame
        The long, short, and do nothing signals for each ticker and date
    lookahead_returns : DataFrame
        The lookahead log returns for each ticker and date
    
    Returns
    -------
    signal_return : DataFrame
        Signal returns for each ticker and date
    """
    return signal*lookahead_returns

project_tests.test_get_signal_return(get_signal_return)
Tests Passed

查看数据

继续使用之前的前瞻价格查看信号收益率。与之前一样,信号收益率的坐标轴位于图表的右侧。

In [16]:
title_string = '{} day LookaheadSignal Returns for {} Stock'
signal_return_5 = get_signal_return(signal_5, price_return_5)
signal_return_10 = get_signal_return(signal_10, price_return_10)
signal_return_20 = get_signal_return(signal_20, price_return_20)
project_helper_zh.plot_signal_returns(
    close[apple_ticker],
    [
        (signal_return_5[apple_ticker], signal_5[apple_ticker], 5),
        (signal_return_10[apple_ticker], signal_10[apple_ticker], 10),
        (signal_return_20[apple_ticker], signal_20[apple_ticker], 20)],
    [title_string.format(5, apple_ticker), title_string.format(10, apple_ticker), title_string.format(20, apple_ticker)])

显著性检验

直方图

下面绘制信号收益率的直方图。

In [17]:
project_helper_zh.plot_signal_histograms(
    [signal_return_5, signal_return_10, signal_return_20],
    'Signal Return',
    ('5 Days', '10 Days', '20 Days'))

问题:从直方图中能看出信号收益率有哪些特征?

#TODO:请在此单元格中填写答案

离群值

你可能在 10 天和 20 天直方图中看到了一些离群值。为了更好地可视化这些离群值,我们将 5 天、10 天和 20 天信号收益率与正态分布的信号收益率进行比较(每个信号收益率分布的均值和标准差都一样)。

In [18]:
project_helper_zh.plot_signal_to_normal_histograms(
    [signal_return_5, signal_return_10, signal_return_20],
    'Signal Return',
    ('5 Days', '10 Days', '20 Days'))

Kolmogorov-Smirnov 检验

发现直方图中的离群值后,我们需要找到导致这些离群收益率的股票。我们将使用 Kolmogorov-Smirnov 检验(简称 KS-检验)。我们会将此检验应用到存在做多或做空信号的每个股票信号收益率上。

In [19]:
# Filter out returns that don't have a long or short signal.
long_short_signal_returns_5 = signal_return_5[signal_5 != 0].stack()
long_short_signal_returns_10 = signal_return_10[signal_10 != 0].stack()
long_short_signal_returns_20 = signal_return_20[signal_20 != 0].stack()

# Get just ticker and signal return
long_short_signal_returns_5 = long_short_signal_returns_5.reset_index().iloc[:, [1,2]]
long_short_signal_returns_5.columns = ['ticker', 'signal_return']
long_short_signal_returns_10 = long_short_signal_returns_10.reset_index().iloc[:, [1,2]]
long_short_signal_returns_10.columns = ['ticker', 'signal_return']
long_short_signal_returns_20 = long_short_signal_returns_20.reset_index().iloc[:, [1,2]]
long_short_signal_returns_20.columns = ['ticker', 'signal_return']

# View some of the data
long_short_signal_returns_5.head(10)
Out[19]:
ticker signal_return
0 A 0.00732604
1 ABC 0.01639650
2 ADP 0.00981520
3 AGENEN 0.02654288
4 AKAM 0.04400495
5 ALGN 0.01545561
6 APC 0.00305859
7 ARMENA 0.03076045
8 BA 0.08061297
9 BAKERI 0.02289554

上述代码会提供要在 KS-检验中使用的数据。

下面实现函数 calculate_kstest 以使用 Kolmogorov-Smirnov 检验(KS 检验)对比正态分布和每个股票的信号收益率分布。针对每个股票的信号收益率在正态分布上运行 KS 检验。使用 scipy.stats.kstest 进行 KS 检验。在计算信号收益率的标准差时,请将自由度设为 0。

对于此函数,不建议寻找向量化解。请迭代更新 groupby 函数。

In [20]:
from scipy.stats import kstest


def calculate_kstest(long_short_signal_returns):
    """
    Calculate the KS-Test against the signal returns with a long or short signal.
    
    Parameters
    ----------
    long_short_signal_returns : DataFrame
        The signal returns which have a signal.
        This DataFrame contains two columns, "ticker" and "signal_return"
    
    Returns
    -------
    ks_values : Pandas Series
        KS static for all the tickers
    p_values : Pandas Series
        P value for all the tickers
    """
    ks_dict = {}
    p_dict = {}
    mean = long_short_signal_returns.mean()
    std = long_short_signal_returns.std(ddof=0)
    for signal_return in long_short_signal_returns.groupby('ticker'): # signal_return[0]=ticker, signal_return[1]=signal_return
        value = signal_return[1]['signal_return'].values
        ks, p = kstest(value, 'norm', args=(mean, std)) # performs a test of the distribution F(x) of an observed random variable against a given distribution G(x). Under the null hypothesis, the two distributions are identical, F(x)=G(x). The alternative hypothesis can be either ‘two-sided’ (default), ‘less’ or ‘greater’. 
        ks_dict[signal_return[0]] = ks
        p_dict[signal_return[0]] = p
    return pd.Series(ks_dict), pd.Series(p_dict)

project_tests.test_calculate_kstest(calculate_kstest)
Tests Passed

查看数据

使用在上面创建的信号收益率计算 ks 和 p 值。

In [21]:
ks_values_5, p_values_5 = calculate_kstest(long_short_signal_returns_5)
ks_values_10, p_values_10 = calculate_kstest(long_short_signal_returns_10)
ks_values_20, p_values_20 = calculate_kstest(long_short_signal_returns_20)

print('ks_values_5')
print(ks_values_5.head(10))
print('p_values_5')
print(p_values_5.head(10))
ks_values_5
A      0.17160539
AAL    0.10749507
AAP    0.19644362
AAPL   0.15590079
ABBV   0.16763349
ABC    0.21421039
ABT    0.21319957
ACN    0.28173215
ADBE   0.24220481
ADI    0.19383767
dtype: float64
p_values_5
A      0.18983039
AAL    0.72369962
AAP    0.04592285
AAPL   0.24554893
ABBV   0.25005315
ABC    0.02723228
ABT    0.04919314
ACN    0.00597397
ADBE   0.00931827
ADI    0.10025426
dtype: float64

查找离群值

计算 ks 和 p 值后,我们看看哪些股票是离群值。实现 find_outliers 函数以查找以下离群值:

  • 通过零假设的代码,即 p 值小于 pvalue_threshold
  • KS 值大于 ks_threshold 的代码。
In [22]:
def find_outliers(ks_values, p_values, ks_threshold, pvalue_threshold=0.05):
    """
    Find outlying symbols using KS values and P-values
    
    Parameters
    ----------
    ks_values : Pandas Series
        KS static for all the tickers
    p_values : Pandas Series
        P value for all the tickers
    ks_threshold : float
        The threshold for the KS statistic
    pvalue_threshold : float
        The threshold for the p-value
    
    Returns
    -------
    outliers : set of str
        Symbols that are outliers
    """
    ks = set(ks_values[ks_values>ks_threshold].index)
    p = set(p_values[p_values<pvalue_threshold].index)
    
    return ks & p


project_tests.test_find_outliers(find_outliers)
Tests Passed

查看数据

使用你实现的 find_outliers 函数看看我们查找到哪些代码。

In [23]:
ks_threshold = 0.8
outliers_5 = find_outliers(ks_values_5, p_values_5, ks_threshold)
outliers_10 = find_outliers(ks_values_10, p_values_10, ks_threshold)
outliers_20 = find_outliers(ks_values_20, p_values_20, ks_threshold)

outlier_tickers = outliers_5.union(outliers_10).union(outliers_20)
print('{} Outliers Found:\n{}'.format(len(outlier_tickers), ', '.join(list(outlier_tickers))))
24 Outliers Found:
SYLVES, ORPHAN, PRAEST, VVEDEN, HUMILI, AGENEN, GESNER, KAUFMA, KOLPAK, ARMENA, SPRENG, BAKERI, BIFLOR, ALTAIC, GREIGI, TARDA, URUMIE, LINIFO, TURKES, SAXATI, CLUSIA, PULCHE, SCHREN, DASYST

显示没有离群值的信号统计显著性

将没有离群值的 5 天、10 天和 20 天信号收益率与正态分布进行比较,并且看看在删除离群值后,p 值有何变化。

In [24]:
good_tickers = list(set(close.columns) - outlier_tickers)

project_helper_zh.plot_signal_to_normal_histograms(
    [signal_return_5[good_tickers], signal_return_10[good_tickers], signal_return_20[good_tickers]],
    'Signal Return Without Outliers',
    ('5 Days', '10 Days', '20 Days'))

更符合预期了。收益率更接近正态分布。你已经完成了突破策略的研究阶段,可以提交项目了。